ИСТИНА

We study the spectral boundary problem \begin{gather*} (-1)^n\,y^{(2n)}=\lambda\rho y,\\ y^{(k)}(0)=y^{(k)}(1)=0,\qquad 0\le k<n \end{gather*} where weight function $\rho$ is a distribution from Sobolev space with negative smoothness. Under the assumption that generalized primitive of $\rho$ is a function with degenerate self-similarity it is proved that the set of eigenvalues can be represented by several series with exponential growth. The order of growth and number of series are calculated via parameters of weight $\rho$. By the same technique the asymptotics of counting function of eigenvalues is obtained for wider class of self-adjoint problems $$ (-1)^{n}y^{(2n)}+\left(p_{n-1}y^{(n-1)}\right)^{(n-1)}+\dots+p_0y=\lambda\rho y $$ with suitable boundary conditions.